Surplus at Risk

[shanlane]

Hello,

Is there an error in Jorion's Surplus at Risk calculation on p 433, or possibly just an error with his vocabulary? I see that in the spreadsheet you interpret his "surplus volatility" as "asset volatility" and then assume there is no volatility in the libilities.

Also, in the video, what you call "absolute SaR" seems quite different from absolute VaR. Whereas absolute VaR is volatility*deviate-expected return, you are calling absolute SaR volatility*deviate-total expected surplus (not total INCREASE in surplus). It seems as if your SaR is more of a shortfall measure to see whether or not the surplus will be positive at the end of the time period whereas absolute VaR is measuring a possible change.

I guess what I am trying to ask is: Should absolute VaR and absolute SaR be calculated the same way (volatility*deviate-expected increase or drift) or is the absolute SaR actually supposed to be a measure of whether or not the TOTAL surplus at the end of the period is positive or nagative? I know this may just come down to vocabulary, so I just want to make sure I understand what is being asked

Thanks!

Shannon

 

[David Harper CFA FRM]

Hi Shannon,

Yes, exactly. Perfect summary. SAR is a burr in my saddle, I've included the SAR issue for the last five (5!?) years to GARP's attention (I will now copy it over to our public for-GARP's-input forum).

Re: I see that in the spreadsheet you interpret his "surplus volatility" as "asset volatility":
yes, good catch. I absolutely decided to do alter that, based on years of confusion. Jorion says the "volatility of the surplus" is 9.4%, then produces a (relative) SAR with 9.4% * 2.33 * $1,000 assets, not than 9.4% * 2.33 * $100 surplus. I realize he has, separately, return of surplus "scaled by assets" but nobody has shown yet why that would resolve. It seems to me that we can do any of three but the terminology should be either: asset volatility, liability volatility, or surplus volatility. His terminology doesn't make sense to me.

Re: absolute/relative: I cannot disagree with your interpretation. Great job specifying absolute VaR, don't let SaR confuse your correct view of absolute VaR! I would really like GARP to decide. You'll notice page 44 shows there are, to my thinking, three ways to characterize the SaR. I think this year I will drop the "absolute" from page 43, I don't think it helps?

My thinking in illustrating Jorion numbers:
T0 surplus = $100
expected growth (drift) = $50
relative SaR = $218.68

application of Absolute VaR in a consistent manner implies: -drift + volatility*deviate = -50 + $218 = $168.68 loss
I called it "absolute VaR" because T0 surplus $100 - $168 loss = -$68.68 shortfall
... see how, in my view on the slide, 168 absolute VaR is identical to a $68.68 shorfall

Exam-wise, I think the burden is on GARP to be specific. I think "shortfall" and "relative SaR = SaR" are the least unclear terms of the lot. Thanks,

 

[shanlane]

Thank you. I am in complete agreement about how to define relative SaR and shortfall. The part that just seems strange is saying"Absolute SaR" and "shortfall" are equal. Is this what you are referring to when you say the nomenclature is not terribly well defined?

Everything else makes perfect sense.

Thanks again for all of the great advice!
Shannon

 

[David Harper CFA FRM]

Hi Shannon, I think "shortfall" is maybe well-defined (i.e., PV of assets - liabilities) as I think it refers to a deficit but
(i) I do regret the "absolute SaR" label in the video/notes and will remove it the revised video b/c I think your first point is correct, that it is confusing and
(ii) I do think absolute SaR is not well defined due to its possible interpretation in fully three ways.

But, exam-wise, I think the request to GARP is simply to define surplus at risk (SaR) ... because you and I seem to agree the "relative VaR" (e.g., $218.68 in Jorion's) is well defined. But, after all of these years, if the request is simply for "surplus at risk" I can give you four definitions (two of which are Jorion's inconsistency from textbook to handbook; in the handbook, Jorion likens SaR to "the potential shortfall in surplus over the horizon" which doesn't seem to match the assignment example?!!)

when i revise it for the upcoming video (and I'll check back with the notes), I think i will just retain the relative SaR (and shortfall) and omit any other SaR reference, using the detail instead. I hope that doesn't add confusion!